Introduction
OZ Pitch Names Defined
Rationale for OZ Pitch Names
Potential Advantages of OZ Pitch Names
Coda
References
Update History

Introduction

For additional information on the OZ pitch-naming convention, see the articles: Learning OZ Pitch Names and Twelve Circular Poems on the Letters O through Z.

OZ Pitch Names Defined

For the OZ pitch-naming convention, the uppercase letters O through Z are used for pitch-class names. The letter O is used in place of the letter C. P is used in place of C-sharp (C#) or D-flat (Db). The following table shows the relationship between OZ pitch-class names and traditional pitch-class names:
 
 

Octave Names

For the OZ pitch-naming convention, the numeral 4 is used as the name of the octave that contains the pitches that would be called "middle C" and "concert A", traditionally.

Progressively lower (higher) octaves are named using progressively lower (higher) numbers. For example, the octave that contains frequencies that are half (twice) the size of those in octave 4 is called "octave 3" ("octave 5").

For the eleven octaves immediately below octave 0, the following uppercase letters are used in order, from lowest frequency to highest: A, B, C, D, E, F, G, H, J, K and L.

For the twelve octaves immediately above octave 9, the following uppercase letters are used in order, from lowest frequency to highest: N, P, Q, R, S, T, U, V, W, X, Y and Z.

Pitch Names

For the OZ pitch-naming convention, the name of a given pitch is formed by concatenating the associated pitch-class name with the associated octave name. For example, the OZ pitch name of the pitch that is traditionally called "middle C" is O4. The OZ pitch name of the pitch that is traditionally called "concert A" is X4. A complete list of the OZ pitch names from OH through ZN with corresponding frequencies is given in the following table for the case when X4 is 440 Hz (Note: The frequencies given in this table are approximate as they have been rounded to two decimal places.):
 
 

OH 1.02	PH 1.08	QH 1.15	RH 1.22	SH 1.29	TH 1.36	UH 1.45	VH 1.53	WH 1.62	XH 1.72	YH 1.82	ZH 1.93
OJ 2.04	PJ 2.17	QJ 2.29	RJ 2.43	SJ 2.58	TJ 2.73	UJ 2.89	VJ 3.06	WJ 3.24	XJ 3.44	YJ 3.64	ZJ 3.86
OK 4.09	PK 4.33	QK 4.59	RK 4.86	SK 5.15	TK 5.46	UK 5.78	VK 6.12	WK 6.49	XK 6.88	YK 7.28	ZK 7.72
OL 8.18	PL 8.66	QL 9.18	RL 9.72	SL 10.30	TL 10.91	UL 11.56	VL 12.25	WL 12.98	XL 13.75	YL 14.57	ZL 15.43
O0 16.35	P0 17.32	Q0 18.35	R0 19.45	S0 20.60	T0 21.83	U0 23.12	V0 24.50	W0 25.96	X0 27.50	Y0 29.14	Z0 30.87
O1 32.70	P1 34.65	Q1 36.71	R1 38.89	S1 41.20	T1 43.65	U1 46.25	V1 49.00	W1 51.91	X1 55.00	Y1 58.27	Z1 61.74
O2 65.41	P2 69.30	Q2 73.42	R2 77.78	S2 82.41	T2 87.31	U2 92.50	V2 98.00	W2 103.83	X2 110.00	Y2 116.54	Z2 123.47
O3 130.81	P3 138.59	Q3 146.83	R3 155.56	S3 164.81	T3 174.61	U3 185.00	V3 196.00	W3 207.65	X3 220.00	Y3 233.08	Z3 246.94
O4 261.63	P4 277.18	Q4 293.66	R4 311.13	S4 329.63	T4 349.23	U4 369.99	V4 392.00	W4 415.30	X4 440.00	Y4 466.16	Z4 493.88
O5 523.25	P5 554.37	Q5 587.33	R5 622.25	S5 659.26	T5 698.46	U5 739.99	V5 783.99	W5 830.61	X5 880.00	Y5 932.33	Z5 987.77
O6 1046.50	P6 1108.73	Q6 1174.66	R6 1244.51	S6 1318.51	T6 1396.91	U6 1479.98	V6 1567.98	W6 1661.22	X6 1760.00	Y6 1864.66	Z6 1975.53
O7 2093.00	P7 2217.46	Q7 2349.32	R7 2489.02	S7 2637.02	T7 2793.83	U7 2959.96	V7 3135.96	W7 3322.44	X7 3520.00	Y7 3729.31	Z7 3951.07
O8 4186.01	P8 4434.92	Q8 4698.64	R8 4978.03	S8 5274.04	T8 5587.65	U8 5919.91	V8 6271.93	W8 6644.88	X8 7040.00	Y8 7458.62	Z8 7902.13
O9 8372.02	P9 8869.84	Q9 9397.27	R9 9956.06	S9 10548.08	T9 11175.30	U9 11839.82	V9 12543.85	W9 13289.75	X9 14080.00	Y9 14917.24	Z9 15804.27
ON 16744.04	PN 17739.69	QN 18794.55	RN 19912.13	SN 21096.16	TN 22350.61	UN 23679.64	VN 25087.71	WN 26579.50	XN 28160.00	YN 29834.48	ZN 31608.53

Note: The frequency that is associated with each named pitch will depend upon the particular tuning standard that is used. Generally, the frequency of O4 will be in the neighborhood of 256 Hz, and pitches will be determined relative to the frequency that is selected for X4, by some convention.

Rationale for OZ Pitch Names

The symbols for OZ pitch-class names have been taken from the English alphabet because, for many, these are familiar symbols. And, there is a convention for ordering these symbols. Letters have been drawn from the end of the alphabet rather than from the beginning, to avoid confusion with traditional pitch names, for which letters A through G are used.

The letters O through Z have been assigned in order, to the twelve pitches of the equal tempered scale. This has been done to simplify the task of learning the pitch class that is associated with each scale degree.

Uppercase letters have been used instead of lowercase letters because it is believed that the uppercase style of these letters might be more easily recognizable.

Octave Names

With one popular existing pitch-naming convention, Hindu-Arabic numerals are used for octave names. In this convention, octaves are numbered consecutively, from lowest frequency to highest, and the numeral 4 is used for the octave that contains middle C. This same approach has been adopted as the basis for naming octaves in the OZ pitch-naming convention.

For most musical purposes, the existing convention is adequate because it spans almost the entire range of frequencies that can be heard by humans. However, there might be applications for which one would like to refer to frequencies that are below or above this range. First, frequencies in the range 1 Hz to 16 Hz (which can be felt rather than heard) are used in the soundtracks of films. Second, humans can hear frequencies above Z9 (approx. 15.8 kHz). Third, one might choose to use the equal tempered scale to analyze the sonic productions of animals (e.g. whales and elephants) that generate sound in the infrasonic or ultrasonic frequency ranges. Or, one might choose to compose music for such non-human listeners. To allow for these possibilities, in the OZ pitch-naming convention, octave names have been specified for a large range of infrasonic and ultrasonic frequencies. If X4 is 440 Hz, then the frequencies of the lowest and highest OZ pitches (i.e. OA and ZZ) will be .00798 Hz (1 cycle per 125.25 seconds) and 64.73 MHz, respectively.

For these extreme octaves, uppercase letters of the English alphabet have been used, again because they are familiar and there is an ordering convention. The letters O and I have not been used for octave names because they look like the numerals 0 and 1, respectively. The letter M has been omitted because it sounds like N. The remaining letters were divided roughly in half with lower (higher) letters to be used for lower (higher) octaves as follows:

A B C D E F G H J K L 0 1 2 3 4 5 6 7 8 9 N P Q R S T U V W X Y Z

When divided in this way, there are 11 named extreme low octaves (A through L, excluding I) and 12 named extreme high octaves (N through Z, excluding O). There are more named high octaves because N was used for a high octave rather than a low octave. This has been done to prevent the symbol P (which is already used for pitch-class names) from being re-used for an octave that might be used often by virtue of the fact that it overlaps with the extreme upper range of human hearing. As a consequence of these decisions, the letters that are (or have been) used for pitch-class names (i.e. letters O through Z in the OZ pitch-naming convention and letters A though G in the traditional pitch-naming convention) are not used to name the octaves in the range 1 Hz through 31.6 kHz. This range contains all frequencies that are commonly used for making music that is intended for human listeners.

In choosing between M and N, M was a less desirable name for the lowest ultrasonic octave than N because in the conventional ordering, M immediately follows L, and L has been used for the highest infrasonic octave (which is far from the lowest ultrasonic octave). Also, N was preferred over M because the symbol N is simpler (i.e. it contains fewer linear strokes) than M.

Pitch Names

For OZ pitch names, the pitch-class name is followed by the octave name. This was done to be consistent with existing pitch-naming conventions whereby a traditional pitch-class name is followed by an octave number.

Potential Advantages of OZ Pitch Names

In some cases, two symbols must be used for a traditional pitch-class name. For 5 of the 12 pitch classes of the equal tempered scale, the pitch-class name consists of a letter followed by an accidental (i.e. a sharp (#) or flat (b) symbol). OZ pitch-class names are more compact because only one symbol is used for each pitch-class name. For this reason alone, OZ pitch names might be easier to read and write.

When pitch-classes are represented by letters, it is possible to create mnemonic devices that are based on words. Such devices may be used to memorize various properties of a given pitch-naming convention. This has been done to some degree with traditional pitch-class names. For example, there are the mnemonic devices "Every Good Boy Does Fine" and "FACE" to memorize the pitch-class names associated with the lines (i.e. E, G, B, D and F) and spaces (i.e. F, A, C and E) of the five-line treble staff on which music is notated, traditionally. But the extent to which this approach may be applied with traditional pitch-class names is limited by the fact that with this convention, 5 of the 12 pitch classes of the equal tempered scale are not represented by a unique letter. In contrast, with the OZ pitch-naming convention, each of the 12 pitch classes is represented by a letter. Consequently, it is possible to employ word-based mnemonic devices to a greater extent with this convention. Thus, it might be possible to learn the OZ pitch-naming convention more easily. For additional information on mnemonic devices for the OZ pitch-naming convention, see the article: Learning OZ Pitch Names.

For most pitch-naming conventions in which traditional pitch-class names are used, octaves begin at C pitches, while the sequence of pitch-class names begins at A. That is, a C is the lowest pitch of each octave, while the conventional order of the letters used for traditional pitch-class names (i.e. A, B, C, D, E, F and G) begins with A. With the OZ pitch-naming convention, both the octaves and pitch-class name sequences are based at O. Octaves begin at O pitches and the conventional order of the letters used for OZ pitch-class names (i.e. O, P, Q, R, S, T, U, V, W, X, Y and Z) also begins with O. In this way, the OZ pitch-naming convention is simpler, and perhaps easier to learn than existing pitch-naming conventions.

When traditional pitch-class names are used as a basis for pitch names, a given frequency may have more than one name. For example, each F# pitch is also a Gb pitch. In all, there are 17 different traditional pitch-class names distributed among 12 different pitch classes. With the OZ pitch-naming convention, there is a one-to-one correspondence between named frequencies and pitch names. Each pitch class has exactly one name, and each named frequency has exactly one name. Because of this, it might be easier to read music notation (either text-based or graphical) that is based on the OZ pitch-naming convention, once this convention has been learned.

For the same reason, music might be easier to notate by using the OZ pitch-naming convention. Generally, the particular name that is used for a given pitch will depend upon the context in which the pitch occurs. When notating music, one takes care to select the particular pitch names that are believed to be the easiest to read. For example, one would probably write F# (rather than Gb) after a D because the melodic interval D-F# is a major third, which is more common than the alternative interval D-Gb (a diminished fourth). With the OZ pitch-naming convention, one need not give any consideration to such matters because there is only one name for each pitch.

Coda

In his system, Rootsey used the 24 lowercase letters from a through z, excluding j and u to label the 24 pitches in the two contiguous octaves that begin with what is traditionally called the C above middle C. This sequence of letters was also used for the two octaves below this range, with the addition of an underscore. The following table shows the correspondence between the pitch names in the OZ pitch-naming convention and those proposed by Rootsey:
 
 

O3 a	P3 b	Q3 c	R3 d	S3 e	T3 f	U3 g	V3 h	W3 i	X3 k	Y3 l	Z3 m
O4 n	P4 o	Q4 p	R4 q	S4 r	T4 s	U4 t	V4 v	W4 w	X4 x	Y4 y	Z4 z
O5 a	P5 b	Q5 c	R5 d	S5 e	T5 f	U5 g	V5 h	W5 i	X5 k	Y5 l	Z5 m
O6 n	P6 o	Q6 p	R6 q	S6 r	T6 s	U6 t	V6 v	W6 w	X6 x	Y6 y	Z6 z

References

Update History